From 8b3f0fc780c0129b67c03164d51ca38c96504a3a Mon Sep 17 00:00:00 2001 From: Giovanni Alzetta Date: Tue, 11 Dec 2018 12:03:27 +0100 Subject: [PATCH] Changed paragraph order in step-60 --- examples/step-60/step-60.cc | 59 ++++++++++++++++++------------------- 1 file changed, 28 insertions(+), 31 deletions(-) diff --git a/examples/step-60/step-60.cc b/examples/step-60/step-60.cc index ff958d9694..9d8e783960 100644 --- a/examples/step-60/step-60.cc +++ b/examples/step-60/step-60.cc @@ -683,36 +683,6 @@ namespace Step60 DoFHandler>>( *embedded_configuration_dh, embedded_configuration); - // In order to construct a well posed coupling interpolation operator $C$, - // there are some constraints on the relative dimension of the grids between - // the embedding and the embedded domains. The coupling operator $C$ and the - // spaces $V$ and $Q$ have to satisfy an inf-sup condition in order for the - // problem to have a solution. It turns out that the non-matching $L^2$ - // projection satisfies such inf-sup, provided that the spaces $V$ and $Q$ - // are compatible between each other (for example, provided that they are - // chosen to be the ones described in the introduction). - // - // However, the *discrete* inf-sup condition must also hold. No - // complications arise here, but it turns out that the discrete inf-sup - // constant deteriorates when the non-matching grids have local diameters - // that are too far away from each other. In particular, it turns out that - // if you choose an embedding grid which is *finer* with respect to the - // embedded grid, the inf-sup constant deteriorates much more than if you - // let the embedded grid be finer. - // - // In order to avoid issues, in this tutorial we will throw an exception if - // the parameters chosen by the user are such that the maximal diameter of - // the embedded grid is greater than the minimal diameter of the embedding - // grid. - // - // This choice guarantees that almost every cell of the embedded grid spans - // no more than two cells of the embedding grid, with some rare exceptions, - // that are negligible in terms of the resulting inf-sup. - const double embedded_space_maximal_diameter = - GridTools::maximal_cell_diameter(*embedded_grid, *embedded_mapping); - double embedding_space_minimal_diameter = - GridTools::minimal_cell_diameter(*space_grid); - setup_embedded_dofs(); // In this tutorial program we not only refine $\Omega$ globally, @@ -814,7 +784,34 @@ namespace Step60 space_grid->execute_coarsening_and_refinement(); } - embedding_space_minimal_diameter = + // In order to construct a well posed coupling interpolation operator $C$, + // there are some constraints on the relative dimension of the grids between + // the embedding and the embedded domains. The coupling operator $C$ and the + // spaces $V$ and $Q$ have to satisfy an inf-sup condition in order for the + // problem to have a solution. It turns out that the non-matching $L^2$ + // projection satisfies such inf-sup, provided that the spaces $V$ and $Q$ + // are compatible between each other (for example, provided that they are + // chosen to be the ones described in the introduction). + // + // However, the *discrete* inf-sup condition must also hold. No + // complications arise here, but it turns out that the discrete inf-sup + // constant deteriorates when the non-matching grids have local diameters + // that are too far away from each other. In particular, it turns out that + // if you choose an embedding grid which is *finer* with respect to the + // embedded grid, the inf-sup constant deteriorates much more than if you + // let the embedded grid be finer. + // + // In order to avoid issues, in this tutorial we will throw an exception if + // the parameters chosen by the user are such that the maximal diameter of + // the embedded grid is greater than the minimal diameter of the embedding + // grid. + // + // This choice guarantees that almost every cell of the embedded grid spans + // no more than two cells of the embedding grid, with some rare exceptions, + // that are negligible in terms of the resulting inf-sup. + const double embedded_space_maximal_diameter = + GridTools::maximal_cell_diameter(*embedded_grid, *embedded_mapping); + double embedding_space_minimal_diameter = GridTools::minimal_cell_diameter(*space_grid); deallog << "Embedding minimal diameter: " -- 2.39.5